Let f(x)={sin⁡xx,x≠0,1,x=0,g(x)=x2−1,f(x)=\begin{cases}\dfrac{\sin x}{x}, & x\neq0,\\1, & x=0,\end{cases}\qquad g(x)=x^{2}-1,…

Mathematics

Problem

Let f(x)={sin⁡xx,x≠0,1,x=0,g(x)=x2−1,f(x)=\begin{cases}\dfrac{\sin x}{x}, & x\neq0,\\1, & x=0,\end{cases}\qquad g(x)=x^{2}-1, and define H(x)=f(x)+x2g(x).H(x)=\frac{f(x)+x^{2}}{g(x)}. For which real values of xx is HH NOT continuous? a) x=0x=0 only b) x=±1x=\pm1 only c) x=0, ±1x=0,\,\pm1 d) HH is continuous for all real xx

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